Estimation of India ’ s export demand function : The bound test approach

India has been witnessing a rapid growth in exports and gross domestic product (GDP). The paper intends to estimate India’s export demand function using bound test approach to cointegration developed by Pesaran et al. (2001) and examines the causal relationship among the variables applying vector error correction model (VECM) model of Granger causality. test using annual time series data for the period 1980 to 2010. The result shows that there is long run equilibrium relationship between demand for export, world income and relative price of export and trade liberalisation. The long run price and income elasticity have been found to be more than the short run price and income elasticity. The income elasticity is more than unity, both in the short run and in the long run signifying the importance of exports as an engine of economic growth. The price elasticity of demand for India’s export has been found to be less than unity in the short run and close to unity in the long run. The Granger causality test reveals that relative price, world income and trade liberalization Granger cause the demand for export, both in the short run as well as in the long run.


INTRODUCTION
It is generally recognized that export plays an important role in the economic growth of a country by making foreign exchange available to finance imports of energy and necessary inputs.This has also been empirically found in the case of newly industrialized economies (NIEs) and Association of South East Asian Nations (ASEAN).Lewis (1980) emphasized the importance of foreign trade among developing countries for the development of the developing countries, particularly, during the period when economic activities in industrial countries were slowing down.Riedel (1984), however, challenged Lewis's argument by saying that developing countries might still increase their exports through price competition as most of these countries face downward sloping demand for their exports.However his argument was again countered by Faini et al. (1992) who argued that one country can expand its export through devaluation, all the countries cannot.
The whole debate about the subject revolves around the value of income and price elasticity of demand for the developing countries' exports.Export will be more sensitive to world economic activity and may act as an engine of economic growth if the income elasticity of export demand is high.If price elasticity of demand is high, the export will face more competition in the international market.A country may increase its exports by making price more competitive.Thus, a country's growth strategy and particularly its trade policy, to a large extent, will depend upon the precise estimate of price and income elasticity of its export demand.Realizing this fact, a large number of studies were done to estimate the export demand function of developing countries and estimated price and income elasticity of demand.However, no consensus could be arrived at from these studies because of their different estimates about the price and income elasticity of export demand.Some studies found that developing countries have more elastic demand for their exports.Hence, they argued that devaluation might be an important instrument to improve the trade balance (Riedel, 1984;Faini et al.,1992;Reinhart, 1995;Senhadji and Montenegro, 1998).But some other studies estimated low price elasticity of demand for the export of developing countries.Thus, they did not support the argument that devaluation would improve the trade balance of the developing countries (Rose, 1990(Rose, , 1991;;Ostry and Rose, 1992;Bahmani-Oskooee and Alse, 1994).Moreover, different countries have different values of elasticity.Since, effectiveness of policy depends upon the value of elasticity for that country, the study of individual country becomes important.The present study takes the case of India in this perspective.
India, since the implementation of new economic policy in 1991, has been experiencing a high rate of economic growth along with a high rate of export growth.Though the growth slowed down to some extent during the period of Asian currency crisis of 1997, it once again picked up since the beginning of the 21st century.The growth in export can be because of demand side factors or supply side factors or both.Though there are ample literature on export demand function estimating price and income elasticity of demand for the developing countries, not much have been done in the context of India, particularly for the period covering large part of trade liberalization era.Some of the studies that were done in the context of India covered only few years of trade liberalization period (Srinivasan, 1998;Sharma, 2000).The present paper intends to estimate the export demand function for India and estimate the price and income elasticity of export demand because of its substantial implications on trade policy and balance of payments issues.
The paper is organized as follows.Next section briefly presents the export demand function.This is followed by description of econometric methodology used to estimate the demand equation and also to find the causal relation of export with its determinants.Empirical results are discussed in subsequent section.In the end concluding remarks are given.

DATA AND MODEL
To estimate the demand for India's exports, the imperfect substitute model proposed by Goldstein and Khan (1985) has been followed.The model assumes that neither imports nor exports are perfect substitutes of domestic products.Exports are imperfect substitutes in world markets for other countries' domestically produced goods, or for third countries' exports.The conventional demand theory says that, the consumer is postulated to Sultan 11267 maximize utility subject to a budget constraint.In this respect, export demand function is specified as a function of the relative price of exports and the rest of the world's real income.Trade liberalization can affect the price and income elasticity of demand for exports.For example, it could increase the sensitivity of exports to price and income changes by making it easier for producers to shift resources into trade sector; by facilitating structural change and by stimulating efficiency.In order to capture the effect of trade liberalization on price and income elasticity, trade openness measured in terms of trade-GDP ratio has also been included in the model.Thus the export demand function can be expressed as: The description of the variables is as follows; l denotes natural log of the variables; X refers to volume of India's exports PXiPMw is relative price of exports measuring the ratio of price of India's exports to price of world's imports; GDPw is rest of the world real income; OP measures the degree of openness of the economy.It is defined as ratio of value of trade (export plus import) to GDP.
t refers to time period.
In the equation, α 1 is price elasticity and α 2 is real income elasticity of export demand.Based on the theory of demand, α 1 should have negative sign, implying that the demand for India's products in international market will increase with decrease in relative price of India's export; α 2 is expected to have a positive sign, as the demand for India's export is expected to increase with increase in the world income.α 3 is also expected to have positive sign as trade liberalization is supposed to affect demand positively.The model estimation is based on annual data between the years 1980 to 2010.The data have been obtained from UNCTADSTAT (2012) and International Monetary Fund (IMF) International Financial Statistics (various issues).

ECONOMETRIC METHODOLOGY
The study involves three steps to estimate the demand equation for India's exports.In the first step the nature of the data or order of integration of the variables, is examined.This is because if the data is found to be non stationary, as most of the macroeconomic data happen to be, then application of OLS technique may give spurious results.In order to avoid that, stationary test of the variables is required.For this purpose, Augmented Dicky-Fuller test (ADF-test) developed by Dickey andFuller (1979, 1981); and Philips-Perron test (PP test) have been applied.The ADF test is based on the assumption that the error term is statistically independent and has a constant variance.Philips and Perron (1988) developed a generalization of the ADF test procedure that allows for fairly mild assumptions concerning the distribution of errors.While the ADF test corrects for higher order serial correlation by adding the lagged difference term on the right hand side, the PP test makes a correction to the t-statistics of the coefficient from the AR(1) regression to account for the serial correlation in residual term.So, the PP statistics are just modification of the ADF t-statistics that takes into account less restrictive nature of the error process.For this reason, the present study has also conducted PP test to examine the stationary nature of the variables under consideration.
Once the order of integration is known and it is found that all the variables are not stationary but integrated of order equal to or less than one, the presence of long run relationship is examined with the help of bound test approach to cointegration developed by Pesaran et al. (2001).This method has some advantages.One, bound test approach is robust for small size sample.Mah (2000) used Pesaran's approach to estimate disaggregated import demand function for Korea with 18 annual observations.Other examples are from Pattichis (1999) and Tang and Nair (2003).Second, failure to test hypothesis due to endogeneity problem under Engle-Granger method can be resolved through this method.Another advantage associated with it is that it can be used even if all the variables are not integrated of same order.So long as the dependent variable is integrated of order one and explanatory variables are integrated of order not higher than one that is, integrated of order zero or order one or mix of integrated of order zero and order one, there can still be a long run relationship between these variables provided that they are cointegrated.
In order to investigate the presence of long run equilibrium relationship (cointegration) among these variables through bound test approach, the following unrestricted error correction model (UECM) (Equation 2) can be estimated. (2) Where, ∆ represents first difference operator and l natural log of respective variables.βi represent the long run parameters, while represent the short run parameters.To estimate equation 2, the maximum number of lags for the variables in level is set equal to one.The appropriate number of lags for the first differenced variables is determined on the basis of Akaike Information criterion (AIC), from maximum of three lags.After estimating Equation 2 by ordinary least square (OLS) method, the null hypothesis of no cointegartion is examined on the basis of the Wald or F-statistic used to assess the significance of the lagged level explanatory variables included in the equation, that is, H0: β1 = β2 = β3 = β4 = 0; (no cointegration exists) and HA: β1 ≠ β2 ≠ β3 ≠ β4 ≠ 0. (cointegration exists) Pesaran et al. (2001) have provided two sets of critical value bounds.At conventional level of significance of 1, 5 or 10%, if the calculated F-value falls outside the critical bound values, a conclusive inference can be made about accepting or rejecting the null hypothesis of no cointegration among the variables.If the Fvalue is greater than the upper limit of the bound values, we reject the null hypothesis that there is no cointegration among the variables under study.If the F-value is less than the lower limit of the bound value, then we accept the null hypothesis of no cointegration among these variables.However, if the calculated Fvalue falls within the critical bound limits, then the order of integration of the explanatory variables needs to be known before drawing any conclusion.
From the estimated UECM, the long run elasticities are measured from the coefficients of the one lagged level explanatory variables divided by the coefficient of the lagged level dependent variable and then multiplied by minus one.Short run elasticities are measured from the coefficients of the first differenced lagged variables in estimated UECM.To ascertain the goodness of fit of the ARDL model, relevant diagnostic tests are conducted.The diagnostic tests examine the normality, serial correlation and heteroskedasticity associated with the model.RESET test is done to test for specification of the model.

CAUSALITY TEST
there is at least one cointegration relationship among the variables of interest, there must be some causal relationship among the variables (Maddala and Kim, 1998).According to Engle and Granger (1987), if the variables are cointegrated, Granger causality test on the basis of multivariate vector error correction model (VECM) will be more appropriate than the causality within the first difference VAR model.The VECM for inflation can be formulated as: (3) ∆ represents first difference operator, ECTt-1 is the one period lagged error correction term derived from the long term cointegration equation and κt is residual term which is assumed to be normally distributed and white noise.If the coefficient of error correction term is negative and significant, we may infer that world real income and relative price of India's exports are causing change in demand for India's exports in the long run.The short run causality is determined on the basis of joint F-test of the coefficient of the first differenced explanatory variables.Again, to estimate the VECM, the appropriate lag order is selected on the basis of AIC criteria.Further, the appropriateness of the model is examined on the basis of various diagnostic tests.The tests for the stability of the parameters have been done on the basis of cumulative sum of recursive residual (CUSUM) test.

EMPIRICAL RESULTS AND ANALYSES
On the priori, it is difficult to decide which method, ADF test or PP test, is better to examine the stationary nature of the variables.Enders (1995) suggested that it is safe to use both the methods for the purpose to conclude with confidence.Thus, the study used both the tests at level and at first difference.The result is reported in Tables 1  and 2. The ADF result in Table 1 shows that all variables are non stationary at level but are stationary at first difference.The Philips-Perron unit root test shown in Table 2 also confirms the ADF test result.Thus, we may  conclude that all the variables included in the model are integrated of order one that is, I(1).
In order to examine the relationship between the demand for India's export, world economic activity, relative prices of India's export and trade liberalization, the UECM version of ARDL model (Pesaran et al., 2001) with lag three (selected on the basis of AIC shown in Table 3) is estimated.Then following Hendry's general to specific modeling approach (Hendry, 1995), a parsimonious model is selected for equation by gradually deleting the insignificant coefficients.The result of the equation is presented in Table 4.The diagnostic tests like Breusch-Godfrey serial correlation LM test, the ARCH test, Breusch-Pagan-Godfrey test and White test for heteroskedasticity, Jarque-Bera test for normality of the residual term, and Ramsey RESET test for model specification confirm that the equation is correctly specified and error term behaves normally.There is no problem of serial correlation, heteroskedasticity.Random terms are normally distributed and model is correctly specified.
The result of the bound test to examine the presence of long run relationship between export demand, world income, relative price of export and trade liberalization is given in Table 5.The result shows that the computed Fstatistics is greater than the critical upper bound value at 1% level.Thus, we may conclude that there exists a long run stable relationship between these variables.
The result of UECM shows that exports are significantly related to all the three variables as is revealed from the tvalues of the coefficients.The signs of all the coefficients are also consistent with theoretical expectation.The export demand is positively related to world income and trade liberalization and is negatively related to relative price.Table 6 reports the results about the short run and long run income and price elasticity of demand for India's exports.The table shows that the price elasticity of demand in the long run is more than in the short   run.The short run price elasticity is estimated to be much less than unity (-0.45); and long run price elasticity is very close to unity (-0.89).The income elasticity in the short run is estimated at 2.12 and long run income elasticity is estimated to be 2.41.Again the income elasticity of demand is more in the long run than in the short run.
Higher income elasticity of export demand signifies that growth in world economic activity will translate into growth of the export sector and slow down of economic activity in the world will have an adverse effect on export sector (as was argued by Deepak Nayyar for the slow growth of export in early eighties).The result of Granger causality test is shown in Tables 7  and 8.The lag period is selected on the basis of AIC (result not shown here).The diagnostic tests show that there is no problem with the estimates and the model is correctly specified.The residual term is serially independent, homoskedastic and normally distributed.Further, the result of cumulative sum of recursive residual CUSUM (Figure 1) test indicates absence of any instability of the coefficients for most of the sample period as plotting of these curves are confined within the 5% critical bound of the parameter stability.The t-value of error correction term and F-value of first differenced explanatory variables shows that all the explanatory variables like world income, relative price and trade liberalization Granger cause export demand, both, in the long run as well as in the short run.

CONCLUSION AND POLICY IMPLICATIONS
The primary objective of the paper is to estimate India's export demand function and calculate its income and price elasticities taking the possible non stationarity in the data into account.The result shows that there is long run stable relationship between demand for India's export, world income, and relative price of export and trade liberalization and all these factors Granger cause export demand in the short run as well in the long run.The result further shows that the sign of income and price elasticity of export demand is consistent with the theory and many of the studies on the subject and are statistically significant too.The magnitude of income elasticity is much more than unity, both in the short run and in the long run.This implies that the export will continue to grow so long as the world economy grows.Hence export should be treated as an engine of growth and Indian government should continue to follow the export promotion policies.However, the price elasticity of export demand is close to but less than unity.This implies that though the devaluation may help in promoting exports in real terms, it may reduce the foreign exchange earnings.

Table 2 .
Unit root test result (PP test).

Table 3 .
Lag selection for bound test.

Table 4 .
Result of UECM of export demand equation.

Table 5 .
Bound test for cointegration.

Table 6 .
Short run and long run elasticity.

Table 7 .
Estimated VECM of India's export demand.
: *, **Show significant at 1 and 5% respectively.Value in square bracket is probability value.
*Shows significant at 1%.Values square brackets are degrees of freedom.